The proper description of such effects involves a two-step renormalization group analysis [1]}. In the first step, we integrate out modes in a weakly interacting metal to obtain a description along the lines of the fixed point theory above. Then, what were formally repulsive interactions at short-distances may manifest themselves as attractive interactions in certain pairing channels. In the second step, the RG flow of such couplings determines the superconducting instabilities.
